Capacitive accelerometers are typically manufactured from silicon as micro-electromechanical systems (MEMS) devices. These small devices comprise a proof mass moveably mounted relative to a support and sealed so that a gaseous medium trapped inside the device provides damping for the proof mass when it moves in a sensing direction in response to an acceleration being applied. In a capacitive accelerometer, there is typically provided a set of fixed electrodes and a set of moveable electrodes attached to the proof mass, with the differential capacitance between the electrodes being measured so as to detect deflection of the proof mass.
WO 2005/083451 provides an example of a capacitive accelerometer comprising a plurality of inter-digitated electrode fingers extending substantially perpendicular to the sensing direction of the device. Two different sets of fixed electrode fingers form sensing and forcing capacitors. The sensing capacitor fingers are offset compared to the driving capacitor fingers so that when a voltage is applied to the fixed electrode fingers, there is a net attractive force depending on the sign of the voltage difference. The device can be operated in a positive spring rate regime, where the mechanical spring restoring force of the proof mass is greater than the electrostatic attractive force of the capacitor electrodes, or a negative spring rate regime, where the electrostatic force exceeds the mechanical restoring force e.g. when higher voltages are applied to the fixed capacitor electrodes. A null position is achieved for the proof mass, where the electrostatic forces match the mechanical spring restoring forces and inertial forces.
In one approach, the same electrode fingers can be used for both driving and sensing. For example, time division multiplexing can be used, where a certain portion of time is spent in sensing displacement of the proof mass and the remaining time is spent in driving the capacitor electrodes. However, without continuous sensing the null condition may not be calculated accurately and therefore noise will typically be high.
In another approach, a pulse width modulation (PWM) technique may be used to control the voltage waveforms supplied to the driving electrodes. An in-phase PWM waveform is applied to a first set of fixed electrodes while an anti-phase PWM waveform is applied to a second set of fixed electrodes. In such a PWM regime the mark/space ratio varies with applied acceleration and provides a linear measure of acceleration. If there is a net force acting on the proof mass then the output signal includes an error bias representing how far away from the null position the proof mass is. This output signal may be used by a PWM servo to define the mark/space ratio applied by a PWM generator.
In WO 2005/083451 a PWM servo adjusts the time difference of the mark/space ratio of the PWM signals driving the electrode fingers. This linearises the output of the accelerometer with input acceleration. The magnitude of the in-phase and anti-phase PWM waveforms applied to the electrodes by the PWM generator is set at a constant reference voltage Vref, typically 25V. This voltage Vref is a constant fixed voltage because it defines the gain accuracy of the accelerometer. The fixed voltage Vref also ensures that the PWM mark/space ratio is a linear function of applied acceleration, so it is important to keep Vref constant. Varying the voltage Vref would give rise to a force depending on Vref2, which would give an undesirable non-linearity. In practice, the fixed value of Vref determines the operational g range of the accelerometer.
The use of a PWM approach allows both sensing and forcing at the same time. Sensing is achieved by detecting the voltage on the proof mass. During the in-phase PWM drive period the proof mass voltage is given by the gap with respect to the first set of electrodes and during the second half cycle anti-phase PWM drive period, the proof mass voltage is given by the gap with respect to the second electrode set. The difference in voltage between the first and second half cycles gives a measure of the offset of the proof mass position with respect to the null position. Thus after a completed cycle both sensing and forcing have been obtained.
Variations in the system, such as temperature variations and/or mechanical variations in the construction of the accelerometer, can change the inter-digitation gap between the electrode fingers and the proof mass. Previously such changes were compensated by the varying mark/space ratio, to maintain the proof mass at the null position at all times. The voltage at this operating point may be considered a critical voltage Vcrit. However an open loop accelerometer is unstable at the Vcrit position, meaning that the proof mass will always tend to be biased away from the null position. It is known that the resonance frequency ω of the proof mass determines the open loop gain of an accelerometer. The open loop gain is defined by the detection of the proof mass per unit of acceleration. The gain is proportional to 1/ω2. It is known that open loop gain can be increased by reducing the resonance frequency ω, but this also limits the maximum acceleration g that can be detected. This is because the value of Vcrit varies as ω2, so a lower resonance frequency reduces Vcrit and therefore reduces the maximum acceleration g that can be detected. Above Vcrit, obtaining loop stability becomes progressively harder as the loop is then conditionally stable, so there is an effective maximum voltage, and hence g range, that can be obtained. Many applications require a high g range to be detected so the conventional approach is limited in its practical use.
It would be desirable to improve the accelerometer head gain without reducing resonance frequency. Maximising the head gain implies that the proof mass moves further under an impulse, so that it is there is a bigger signal on the proof mass to act as an error signal for the PWM servo to operate against. This increased head gain will give rise to a better loop lock which is ultimately determined by noise in the system, so a bigger signal to noise ratio may be obtained.
Driving the fixed electrodes at higher voltages, so as to achieve a negative spring rate regime, can increase the g range. However, operating in the negative spring rate regime can also cause difficulty in achieving loop stability, with a poor overall closely frequency response where loop filtering becomes more critical and dependent on the detailed MEMS fabrication tolerances.
It would be desirable to increase the acceleration g range of an accelerometer, without reducing the open loop gain, and to maximize the head gain.